England take on Russia on Saturday having not reached a global or European final since their 1966 World Cup triumph and it is 20 years since they even made a semi-final, also on home soil, in the 1996 Euros.
Generations of England players have talked about how the pressure to break that drought has often been suffocating.
"You can't wipe the slate clean. We'll live with the fact it's been 50 years since we won a tournament but all we can do is hope the players approach this one with a relaxed attitude," Hodgson told a news conference at the sparkling all-white, fully redeveloped 67,000-capacity Velodrome.
"My fear as a coach would be that the players take anxiety on to the field, that they're weighed down when they go out and don't play as well as they like, imagining the headlines.
"We try to encourage them to believe in themselves, go out and play the football we've been trying to play, and we'll see what it brings."
Rooney has seen the best and worst of successive England campaigns since a starring performance in Euro 2004 and, having once been a youngster that no-one could ever have accused of lacking belief, he too was keen to stress the importance of building confidence.
"You can play without fear, naturally, younger lads do that. I did it when I broke into the team in 2003 but it's more of a case of the manager, coaching staff and me telling the players how good they are," he said.
"We have a really talented group of players and we need them to believe that themselves, that they're good enough to go out there and do it. You can see the confidence and ambition and desire in the players, and that's great."
England captain Rooney, with 52 goals in 111 appearances, seems a certain starter but the coach still seems unsure of how best to use him with the likes of Jamie Vardy and Harry Kane more obvious front-line choices.
Having drifted back from striker to something of a number 10, Rooney then played the latter part of the season for Manchester United firmly ensconced in midfield.
A Russian journalist had the temerity to question whether, at 30, Rooney's powers might be on the wane and the captain bristled.
"I know the qualities I have and I don't have to sit here and defend myself," he said, with trademark glare. "I've played this game for a lot of years and I'm aware that my game has changed slightly, in my opinion, for the better.
"I've played in midfield for the last few months at United, and it's a natural way of football. I feel with my football intelligence, I can play there and further my career there as well."
Pushed to say which was his preferred position, Rooney replied: "On the pitch."
(Editing by Ian Chadband)
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